The potential of QSOs as cosmological probes was evident since the identification of the first QSO redshifts in 1963 [1]}, [2]}, [3]}.
Over the last four decades, several techniques employing empirical correlations between various QSO properties have been proposed to gauge cosmological parameters. Striking examples include the relations between the luminosity and spectral properties such as the emission-line equivalent width [4]}, the broad-line region radius [5]}, and the X-ray variability amplitude [6]}. Nonetheless, all these correlations are either affected by a large observational dispersion (up to 0.6 dex) or applicable over a limited redshift range with the current facilities. Other methods [7]}, [8]}, [9]} could be promising, but are still more a proof of concept than a real cosmological tool. For these reasons, QSOs are not yet competitive against standard probes like SNe Ia.
Recently, a new proposed method leverages on the observed non-linear relation between the QSO ultraviolet (at the rest frame 2500 Å, \(L_{\rm UV}\) ) and X-ray (at the rest frame 2 keV, \(L_{\rm X}\) ) emission (e.g., [10]}), parametrised as \(L_{\rm X}\propto L_{\rm UV}^\gamma \) , with an observed slope \(\gamma \simeq 0.6\) .
This relation allows us an independent measurement of the QSO distances (provided an external calibration) and makes possible to extend the distance modulus–redshift relation (or the so-called Hubble-Lemaître diagram) of SNe Ia to a redshift range that is still poorly explored .
The applicability of this methodology is based on two fundamental points. Firstly, the understanding that most of the observed dispersion in the \(L_{\rm X}-L_{\rm UV}\)  relation is not intrinsic to the relation itself but rather due to observational issues (e.g., gas absorption in the X-rays, dust extinction in the UV, calibration uncertainties in the X-rays (e.g., [11]}), variability, selection biases). In fact, with an optimal selection of sources where the intrinsic UV and X-ray QSO emission can be measured, the observed dispersion drops from previously observed 0.4 dex to \(\simeq \) 0.2 dex [12]}, [13]}. As shown in the previous section, the slope of the \(L_{\rm X}-L_{\rm UV}\)  relation does not evolve with redshift up to the highest redshift where the source statistics is currently sufficient to verify any possible dependence of the slope with distance (\(z\simeq 4\) ).
A major implication of the results above mentioned is that the \(L_{\rm X}-L_{\rm UV}\)  relation must be the manifestation of a universal mechanism at work in the QSO engines. Nonetheless, the details on the physical process at the origin of this relation are still unknown (e.g., [14]}, [15]}, [13]}, [17]}, and references therein). In the following, we will focus on the details and the results obtained with this technique.
